Polynomial poly-vector fields

Details Polynomial poly-vector fields Polynomial poly-vector fields

2004-09-09

arxiv.org/abs/math/0409157v4

Int. Electron. J. Geom. 2 (2009), no.1, 55-73

Mathematics

Differential Geometry

20 pages. v4: sections rearranged and formulations clarified

Scientific paper

In this text we give a decomposition result on polynomial poly-vector fields generalizing a result on the decomposition of homogeneous Poisson structures. We discuss consequences of this decomposition result in particular for low dimensions and low degrees. We provide the tools to calculate simple cubic Poisson structures in dimension three and quadratic Poisson structures in dimension four. Our decomposition result has a nice effect on the relation between Poisson structures and Jacobi structures.

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